
<template id="zmn-template">
    <p style="width: min(100%, 80em)">A group of the form ℤ<sub>mn</sub> is isomorphic to the product group
        ℤ<sub>m</sub> × ℤ<sub>n</sub> just when <i>m</i> and <i>n</i> are relatively prime.
        In this case, because ${m} and ${n} are relatively prime, ℤ<sub>${m}</sub> × ℤ<sub>${n}</sub>
        is isomorphic to ℤ<sub>${m*n}</sub>.</p>
</template>

<template id="zmn-prime-template">
    <p style="width: min(100%, 80em)">A group of the form ℤ<sub>mn</sub> is isomorphic to the product group
        ℤ<sub>m</sub> × ℤ<sub>n</sub> just when <i>m</i> and <i>n</i> are relatively prime.
        In this case, <i>mn</i> = ${Group.order}, which gives no possibilities for <i>m</i> and <i>n</i>.</p>
    <p>Thus there is not even a product group  ℤ<sub>m</sub> × ℤ<sub>n</sub>
        to speak of being isomorphic to.  (One of <i>m</i> or <i>n</i>
        would need to be 1, making one factor the trivial group and the other ℤ<sub>mn</sub>.)</p>
</template>

<template id="zmn-nonZmnGroup-template">
    <p style="width: min(100%, 80em)">A group of the form ℤ<sub>mn</sub> is isomorphic to the product group
        ℤ<sub>m</sub> × ℤ<sub>n</sub> just when <i>m</i> and <i>n</i> are relatively prime.
        In this case, the factors of <i>mn</i> are ${facs}, which cannot be divided into
        two non-trivial sets that do not both contain ${factors[0]}.  Thus, there cannot be two relatively prime
        factors of <i>mn</i> since any non-trivial factors must both be divisible by ${factors[0]}.</p>
</template>

<template id="zmn-illustration-template">
    <p><a href="" action="ZmnInfo.show${isZmn?'':'No'}ZmnIsomorphismSheet(${m},${n})">Click here</a> to see
        ${isZmn ? 'an illustration of' : ''} why ℤ<sub>${m * n}</sub> is ${isZmn ? '' : 'not'}
        isomorphic to ℤ<sub>m</sub> × ℤ<sub>n</sub>.</p>
</template>
